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                <ol class="chapter"><li class="chapter-item expanded affix "><a href="intro.html">介绍</a></li><li class="chapter-item expanded "><a href="guide-start.html"><strong aria-hidden="true">1.</strong> 入门指南</a></li><li class="chapter-item expanded "><a href="crates.html"><strong aria-hidden="true">2.</strong> crate 和特性</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="crates-rand.html"><strong aria-hidden="true">2.1.</strong> 随机加密(co)</a></li><li class="chapter-item expanded "><a href="crates-gen.html"><strong aria-hidden="true">2.2.</strong> 随机信号生成器</a></li></ol></li><li class="chapter-item expanded "><a href="guide.html"><strong aria-hidden="true">3.</strong> 指南</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="guide-data.html"><strong aria-hidden="true">3.1.</strong> 随机数据</a></li><li class="chapter-item expanded "><a href="guide-gen.html"><strong aria-hidden="true">3.2.</strong> 生成器类型</a></li><li class="chapter-item expanded "><a href="guide-rngs.html"><strong aria-hidden="true">3.3.</strong> 随机数生成器(RNGs)</a></li><li class="chapter-item expanded "><a href="guide-seeding.html"><strong aria-hidden="true">3.4.</strong> 为随机数生成器置种</a></li><li class="chapter-item expanded "><a href="guide-values.html"><strong aria-hidden="true">3.5.</strong> 随机值</a></li><li class="chapter-item expanded "><a href="guide-dist.html" class="active"><strong aria-hidden="true">3.6.</strong> 各种分布方式</a></li><li class="chapter-item expanded "><a href="guide-seq.html"><strong aria-hidden="true">3.7.</strong> 序列</a></li><li class="chapter-item expanded "><a href="guide-err.html"><strong aria-hidden="true">3.8.</strong> 错误处理</a></li></ol></li><li class="chapter-item expanded "><a href="portability.html"><strong aria-hidden="true">4.</strong> 可移植性</a></li><li class="chapter-item expanded "><a href="update.html"><strong aria-hidden="true">5.</strong> 更新</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="update-0.5.html"><strong aria-hidden="true">5.1.</strong> 更新到 0.5</a></li><li class="chapter-item expanded "><a href="update-0.6.html"><strong aria-hidden="true">5.2.</strong> 更新到 0.6</a></li><li class="chapter-item expanded "><a href="update-0.7.html"><strong aria-hidden="true">5.3.</strong> 更新到 0.7</a></li></ol></li><li class="chapter-item expanded "><a href="contributing.html"><strong aria-hidden="true">6.</strong> 贡献</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="contrib-doc.html"><strong aria-hidden="true">6.1.</strong> 文档</a></li><li class="chapter-item expanded "><a href="contrib-scope.html"><strong aria-hidden="true">6.2.</strong> Scope</a></li><li class="chapter-item expanded "><a href="contrib-test.html"><strong aria-hidden="true">6.3.</strong> 测试</a></li><li class="chapter-item expanded "><a href="contrib-bench.html"><strong aria-hidden="true">6.4.</strong> 基准</a></li></ol></li></ol>
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                        <blockquote>
<p><a href="https://github.com/rust-random/book/blob/master/src/guide-dist.md">guide-dist.md</a><br />
commit: 37f01c4663f960a5af1546d2173afe0e64bf9b2c <br />
本章译文最后维护日期：2020-12-1</p>
</blockquote>
<h1><a class="header" href="#random-distributions" id="random-distributions">Random distributions</a></h1>
<h1><a class="header" href="#随机分布" id="随机分布">随机分布</a></h1>
<p>为了在产生随机值时获得最大的灵活性，我们定义了 <a href="https://rust-random.github.io/rand/rand/distributions/trait.Distribution.html"><code>Distribution</code></a> trait:</p>
<pre><pre class="playground"><code class="language-rust">
<span class="boring">#![allow(unused)]
</span><span class="boring">fn main() {
</span>// T类数据的生产者：
pub trait Distribution&lt;T&gt; {
    // 主函数：
    fn sample&lt;R: Rng + ?Sized&gt;(&amp;self, rng: &amp;mut R) -&gt; T;

    // 使用上面 sample函数的便捷函数：
    fn sample_iter&lt;R&gt;(self, rng: R) -&gt; DistIter&lt;Self, R, T&gt;
    where
        Self: Sized,
        R: Rng,
    { ... }
}
<span class="boring">}
</span></code></pre></pre>
<p>Rand 提供了许多不同的分布(distribution)的实现；我们在这里讨论了其中最常见的几种，要获得完整的细节，请参阅 <a href="https://rust-random.github.io/rand/rand/distributions/index.html"><code>distributions</code></a>模块和 <a href="https://rust-random.github.io/rand/rand_distr/index.html"><code>rand_distr</code></a> crate。</p>
<h1><a class="header" href="#uniform-distributions" id="uniform-distributions">Uniform distributions</a></h1>
<h1><a class="header" href="#均匀分布" id="均匀分布">均匀分布</a></h1>
<p>最直观的分布类型是我们已经讨论过的：一种没有模式的分布，即每个值或值的区间都是等可能的。这就是所谓的“均匀(uniform)”。</p>
<p>Rand 实际上有几个均匀分布变体版本，代表了不同的区间(rang):</p>
<ul>
<li><a href="https://rust-random.github.io/rand/rand/distributions/struct.Standard.html"><code>Standard</code></a> 不需要传入参数，只需要根据输出类型就能在整个类型区间内均匀抽样取值。<a href="https://rust-random.github.io/rand/rand/trait.Rng.html#method.gen"><code>Rng::gen</code></a> 提供了使用此分布的快捷路径。</li>
<li><a href="https://rust-random.github.io/rand/rand/distributions/struct.Uniform.html"><code>Uniform</code></a> 可以通过 <code>Uniform::new(low, high)</code>（包括<code>low</code>，不包括<code>high</code>）的形式来传入参数，或通过 <code>Uniform::new_inclusive(low, high)</code>（两者都包括）来传入参数，并在此范围内均匀抽样。
<a href="https://rust-random.github.io/rand/rand/trait.Rng.html#method.gen_range"><code>Rng::gen_range</code></a> 是在 <a href="https://rust-random.github.io/rand/rand/distributions/struct.Uniform.html#method.sample_single"><code>Uniform::sample_single</code></a> 上定义的一种便捷方法，针对单个样本的使用进行了优化。</li>
<li><a href="https://rust-random.github.io/rand/rand/distributions/struct.Alphanumeric.html"><code>Alphanumeric</code></a> 是在 <code>char</code> 值 <code>0-9A-Za-z</code> 上的均匀分布。</li>
<li><a href="https://rust-random.github.io/rand/rand/distributions/struct.Open01.html"><code>Open01</code></a> 和 <a href="https://rust-random.github.io/rand/rand/distributions/struct.OpenClosed01.html"><code>OpenClosed01</code></a> 为浮点类型提供了备用抽样区间（见下文）</li>
</ul>
<h2><a class="header" href="#uniform-sampling-by-type" id="uniform-sampling-by-type">Uniform sampling by type</a></h2>
<h2><a class="header" href="#按类型均匀抽样" id="按类型均匀抽样">按类型均匀抽样</a></h2>
<p>让我们通过类型来简单浏览一遍各种分布：</p>
<ul>
<li>
<p>对于 <code>bool</code>”，<a href="https://rust-random.github.io/rand/rand/distributions/struct.Standard.html"><code>Standard</code></a>分布以50%的概率对每个值进行抽样。</p>
</li>
<li>
<p>对于 <code>Option&lt;T&gt;</code>，<a href="https://rust-random.github.io/rand/rand/distributions/struct.Standard.html"><code>Standard</code></a>分布以50%的概率抽样 <code>None</code>，另外50%会根据其类型对 <code>Some(value)</code> 进行抽样。</p>
</li>
<li>
<p>对于整数（<code>u8</code> 到 <code>u128</code>、<code>usize</code> 和各类 <code>i*</code>类型），<a href="https://rust-random.github.io/rand/rand/distributions/struct.Standard.html"><code>Standard</code></a>分布从所有可能的值进行抽样，而 <a href="https://rust-random.github.io/rand/rand/distributions/struct.Uniform.html"><code>Uniform</code></a>分布则从入参的区间进行抽样。</p>
</li>
<li>
<p>对于 <code>NonZeroU8</code> 和其他“非零”类型，<a href="https://rust-random.github.io/rand/rand/distributions/struct.Standard.html"><code>Standard</code></a>分布从所有非零值中均匀抽样（拒绝方法）。</p>
</li>
<li>
<p>对于 <code>Wrapping&lt;T&gt;</code> 包装的整数类型，<a href="https://rust-random.github.io/rand/rand/distributions/struct.Standard.html"><code>Standard</code></a>分布的抽样效果跟针对此相应的整型类型效果一样。</p>
</li>
<li>
<p>对于浮点型（<code>f32</code>，<code>f64</code>）</p>
<ul>
<li><a href="https://rust-random.github.io/rand/rand/distributions/struct.Standard.html"><code>Standard</code></a>分布会在半开区间 <code>[0，1)</code> 内抽样，抽样值的精度为24或53bit（分别对应 <code>f32</code> 和 <code>f64</code>）</li>
<li><a href="https://rust-random.github.io/rand/rand/distributions/struct.OpenClosed01.html"><code>OpenClosed01</code></a>分布会在半开区间 <code>(0, 1]</code> 内抽样，抽样值的精度为24或53bit</li>
<li><a href="https://rust-random.github.io/rand/rand/distributions/struct.Open01.html"><code>Open01</code></a>分布会在开区间 <code>(0, 1)</code> 内抽样，抽样值的精度为23或52bit</li>
<li><a href="https://rust-random.github.io/rand/rand/distributions/struct.Uniform.html"><code>Uniform</code></a>分布会在给定的区间内抽样，抽样值的精度为23或52bit</li>
</ul>
</li>
<li>
<p>对于 <code>char</code>类型，<a href="https://rust-random.github.io/rand/rand/distributions/struct.Standard.html"><code>Standard</code></a>分布从所有可用的 Unicode代码点进行均匀抽样；其中许多值可能无法打印（取决于字体支持）。<a href="https://rust-random.github.io/rand/rand/distributions/struct.Alphanumeric.html"><code>Alphanumeric</code></a>分布只对 a-z、a-z 和 0-9 进行均匀抽样。</p>
</li>
<li>
<p>对于元组和数组，在支持的情况下，每个元素都按上述方式进行抽样。
<a href="https://rust-random.github.io/rand/rand/distributions/struct.Standard.html"><code>Standard</code></a>分布和 <a href="https://rust-random.github.io/rand/rand/distributions/struct.Uniform.html"><code>Uniform</code></a>分布都支持批量填充这类类型（元组最多12个元素；数组最多32个元素）。
这包括空元组<code>()</code>和空数组。</p>
</li>
<li>
<p>对于SIMD类型，<a href="https://rust-random.github.io/rand/rand/distributions/struct.Standard.html"><code>Standard</code></a>分布和<a href="https://rust-random.github.io/rand/rand/distributions/struct.Uniform.html"><code>Uniform</code></a>分布对每个元素进行抽样（对于后者，<code>low</code>和<code>high</code>参数<em>也</em>都必须是SIMD类型，以便能有效地同时从多个区间进行抽样）。开启SIMD功能是通过一个<a href="../features.html#simd-support">特性标志位</a>实现的。</p>
</li>
</ul>
<h1><a class="header" href="#non-uniform-distributions" id="non-uniform-distributions">Non-uniform distributions</a></h1>
<h1><a class="header" href="#非均匀分布" id="非均匀分布">非均匀分布</a></h1>
<p>非均匀分布可分为以下两类。一些离散性非均匀分布和所有的连续性非均匀分布目前已经从主要的 <a href="https://rust-random.github.io/rand/rand/index.html"><code>rand</code></a> crate 移动到一个专门的 <a href="https://rust-random.github.io/rand/rand_distr/index.html"><code>rand_distr</code></a> crate 下了。</p>
<h2><a class="header" href="#discrete-non-uniform-distributions" id="discrete-non-uniform-distributions">Discrete non-uniform distributions</a></h2>
<h2><a class="header" href="#离散的非均匀分布" id="离散的非均匀分布">离散的非均匀分布</a></h2>
<p>离散分布从布尔或整数类型上抽样。如上所述，可以均匀地对这些样本进行抽样，或者如下所述，通过非均匀分布进行抽样。</p>
<p>离散分布可能直接从一组离散值（如切片或 <code>enum</code>）中抽样。参见<a href="../guide-seq.html">序列</a>一章中与切片和迭代器类型相关的 trait。Rand 没有提供直接从 <code>enum</code> 中抽样的功能，但 <code>Option</code> 除外（见上文）。</p>
<h3><a class="header" href="#booleans" id="booleans">Booleans</a></h3>
<p><a href="https://rust-random.github.io/rand/rand/distributions/struct.Bernoulli.html"><code>Bernoulli</code></a>分布是一个奇特的名称，用于生成布尔值，其中生成 <code>true</code> 的概率为给定的 <code>p</code>，或者通过比率 <code>success : failure</code> 来定义布尔值的生成比例。这通常用于描述一个<em>成功</em>（<code>true</code>）概率为 <code>p</code> 的<em>试验</em>。</p>
<p>方法<a href="https://rust-random.github.io/rand/rand/trait.Rng.html#method.gen_bool"><code>Rng::gen_bool</code></a>和<a href="https://rust-random.github.io/rand/rand/trait.Rng.html#method.gen_ratio"><code>Rng::gen_ratio</code></a> 是此分布的快捷方式。</p>
<h3><a class="header" href="#integers" id="integers">Integers</a></h3>
<p><a href="https://rust-random.github.io/rand/rand/distributions/struct.Binomial.html"><code>Binomial</code></a>分布与<a href="https://rust-random.github.io/rand/rand/distributions/struct.Bernoulli.html"><code>Bernoulli</code></a>分布有关，因为它模拟了n个独立的试验，每个试验都有成功的概率 <code>p</code>，然后计算成功的次数。</p>
<p>注意，对于较大的 <code>n</code>，['Binomial']分布的实现要比分 <code>n</code>次单独去抽样的试验快很多。</p>
<p><a href="https://rust-random.github.io/rand/rand/distributions/struct.Poisson.html"><code>Poisson</code></a>分布表示在一个固定的时间间隔内发生的事件的预期数量，并假定事件发生的速率为固定的 λ。</p>
<h3><a class="header" href="#weighted-sequences" id="weighted-sequences">Weighted sequences</a></h3>
<h3><a class="header" href="#加权序列" id="加权序列">加权序列</a></h3>
<p><a href="https://rust-random.github.io/rand/rand/distributions/weighted/struct.WeightedIndex.html"><code>WeightedIndex</code></a>分布从权重序列中抽取索引。请参阅<a href="../guide-seq.html">序列</a>章节来了解如何方便地使用包装器直接对切片元素进行采样。</p>
<p>例如，加权抽样可以用于对从一个装有5个绿色、15个红色和80个蓝色弹珠的桶中取样弹珠的颜色的过程进行建模。</p>
<p>目前，Rand库仅实现了<em>带替换的抽样(sampling with replacement)</em>，即假设在相同的初始分布中进行重复抽样（即任何被取走的弹球都被重新放回）。现在已经有一个要求实现*无替换的抽样(sampling without replacement)*分布的<a href="https://github.com/rust-random/rand/issues/596">需求</a>在开发中了。</p>
<p>还要注意 <a href="https://rust-random.github.io/rand/rand/distributions/weighted/struct.WeightedIndex.html"><code>WeightedIndex</code></a> 有两个实现可用；第一个为抽取少量的样本做了相应的优化，而 <a href="https://rust-random.github.io/rand/rand/distributions/weighted/alias_method/struct.WeightedIndex.html"><code>alias_method::WeightedIndex</code></a> 则为抽取大量的样本做了优化（其中的“大”可能意味着“&gt; 1000”；标准推荐）。</p>
<h2><a class="header" href="#continuous-non-uniform-distributions" id="continuous-non-uniform-distributions">Continuous non-uniform distributions</a></h2>
<h2><a class="header" href="#连续性非均匀分布" id="连续性非均匀分布">连续性非均匀分布</a></h2>
<p>连续分布模型样本取自实数线ℝ，在某些情况下也从更高维度（ℝ²、ℝ³等）提取样本。我们在大多数情况下为 <code>f64</code> 和 <code>f32</code>类型的输出提供了连续分布的实现，注意目前 <code>f32</code> 的实现只是降低了 <code>f64</code> 示例的精度。</p>
<p>指数分布 <a href="https://rust-random.github.io/rand/rand/distributions/struct.Exp.html"><code>Exp</code></a> 可以模拟衰减过程，假设衰减率固定（即指数衰减）。</p>
<p><a href="https://rust-random.github.io/rand/rand/distributions/struct.Normal.html"><code>Normal</code></a>分布（也称为高斯分布）用给定的平均值和标准差模拟正态分布（“钟形曲线”）的抽样。<a href="https://rust-random.github.io/rand/rand/distributions/struct.LogNormal.html"><code>LogNormal</code></a>是相关的：对于来自对数正态分布的样本 <code>X</code>，<code>log(X)</code> 是正态分布；这“扭曲”了正态分布，以避免出现负值，并带有一个长的正尾。</p>
<p><a href="https://rust-random.github.io/rand/rand/distributions/struct.UnitCircle.html"><code>UnitCircle</code></a>分布和 <a href="https://rust-random.github.io/rand/rand/distributions/struct.UnitSphereSurface.html"><code>UnitSphereSurface</code></a>分布模拟从圆的边缘或从球面上均匀采样。</p>
<p>['Cauchy']分布（也称为洛伦兹(Lorentz)分布）是角度均匀分布的从点 <code>(x0, γ)</code> 出发的射线相对于x轴的截距的分布。</p>
<p><a href="https://rust-random.github.io/rand/rand/distributions/struct.Beta.html"><code>Beta</code></a>分布是一个双参数概率分布，其输出值在0到1之间。<a href="https://rust-random.github.io/rand/rand/distributions/struct.Dirichlet.html"><code>Dirichlet</code></a>分布是对任何正数个参数的推广。</p>

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